Numerical Simulation of Two-Dimensional Shock/Boundary-Layer Interaction between a Rocket and Booster

A two-dimensional Reynolds-averaged Navier-Stokes solver is applied to analyze the aerodynamic behavior of the Shock/Boundary-Layer interaction of rocket with a boosted The K-ε turbulence model and a finite volume method in a unstructured body-fitted curvilinear coordinates have been used. The results indicate that the separation and the reattachment occur in the Boundary-Layer of the main rocket because of the shock interaction. The shape of the booster nose effects the flow field obviously. In the case of the hemisphere booster nose the pressure has complicate distributions and the separation is very clear. The distance between the booster and main rocket has the evident effect on the flow field. If the distance is smaller the pressure coefficient is bigger the separation zone even the separation bubble occurs.

Model for Asymmetry of Shock/Boundary Layer Interactions in Nozzle Flows

The reason for the asymmetry phenomenon of shock/boundary layer interactions(SBLI)in a completely symmetric nozzle with symmetric flow conditions is still an open question.A model for the asymmetry of nozzle flows was proposed based on the properties of fluid entrainment in the mixing layer and momentum conservation.The asymmetry model is deduced based on the nozzle flow with restricted shock separation,and is still applicable for free shock separation.Flow deflection angle at nozzle exit is deduced from this model.Steady numerical simulations are conducted to model the asymmetry of the SBLIs in a planar convergent-divergent nozzle tested by previous researchers.The obtained values of deflection angle based on the numerical results of forced symmetric nozzle flows can judge the asymmetry of flows in a nozzle at some operations.It shows that the entrainment of shear layer on the separation induced by SBLTs is one of the reasons for the asymmetry in the confined SBLIs.

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

Observations are presented from experiments and calculations where a laminar spherical CH4/air flame is perturbed successively by incident and reflected shock waves. The experiments are performed in a standard shock tube arrangement, in which a high-speed shadowgraph imaging system is used to record evolutions of the flame. Numerical simulations are conducted by using second-order wave propagation algorithms, based on two-dimensional axisymmetric Navier-Stokes equations with detailed chemical reactions. Qualitative agreements are obtained between the experimental and numerical results. Under actions of incident shock waves, Richtmyer-Meshkov instability responsible for the flame deformation is induced in the flame, and the distoned flame takes a barrel shape. Then, under subsequent actions of the shock wave reflected from a planar wall, the flame takes an inclined non-symmetrical kidney shape in a symmetric cross section, which means a mushroom-like shape of the flame comes finally into being. The vorticity direction in the ring cap has been altered by the reflected shock＇s action, which makes the head of the mushroom-like flame extend quickly to the side wall.

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the practicability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disintegrates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17 % occurs with a triangular shape, while the maximum increase in aerodynamic efficiency（lift-to-drag ratio）of around 10 % happens with a rectangular shape at an angle of attack of 2.26？.

THE INTERACTION BETWEEN SHOCK WAVES AND FOAM IN A SHOCK TUBE

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.

Study on Mach stems induced by interaction of planar shock waves on two intersecting wedges

The properties of Mach stems in hypersonic corner flow induced by Mach interaction over 3D intersecting wedges were studied theoretically and numerically.A new method called ＂spatial dimension reduction＂ was used to analyze theoretically the location and Mach number behind Mach stems. By using this approach, the problem of 3D steady shock/shock interaction over 3D intersecting wedges was transformed into a 2D moving one on cross sections, which can be solved by shock-polar theory and shock dynamics theory. The properties of Mach interaction over 3D intersecting wedges can be analyzed with the new method,including pressure, temperature, density in the vicinity of triple points, location, and Mach number behind Mach stems.Theoretical results were compared with numerical results,and good agreement was obtained. Also, the influence of Mach number and wedge angle on the properties of a 3D Mach stem was studied.

Fluid structure interaction for circulation valve of hydraulic shock absorber

Based on the working principle and the damping characteristic of hydraulic shock absorber, a fluid structure interaction method was presented, which was used to analyze the microcosmic and high-frequency processing mechanism of fluid structure interaction between circulation valve and liquid of hydraulic shock absorber. The fluid mesh distortion was controlled by the CEL language, and the fluid struc^tre interaction mathematical model was established. The finite element model was established by ANSYS CFX software and was analyzed by dynamic mesh technique. The local sensitive computational area was meshed by prismatic grid, which could reduce the negative volume problem during the simulation. The circulation valve and liquid of hydraulic shock absorber were simulated and analyzed under the condition of sinusoidal inlet velocity loads. Flow characteristic and dynamics characteristic were obtained. The pressure distribution and the displacement of circulation value were obtained, and the acceleration curve of circulation valve was simulated and analyzed. The conformity of the final simulation results with the experimental datum indicates that this method is accurate and reliable to analyze the dynamics characteristic between circulation valve and liquid of hydraulic shock absorber, which can provide a theoretical foundation for optimizing hydraulic shock absorber in the future.

UNSTEADY INTERACTION OF SHOCK WAVE DIFFRACTING AROUND A CIRCULAR CYLINDER IN AIR

The reflection and diffraction of a planar shock wave around a circular cylinder are a typical problem of the complex nonlinear shock wave phenomena in literature.It has long been studied experimentally,analytically as well as numerically.Takayama in 1987 obtained clear experimental pictures ofisopycnics in shock tube under the condi- tion that the impinging shock wave propagates as far as 3 diameters away from the cylinder.To know more complete- ly the whole unsteady process,it is desirable to get experimental results in a region which is more than 10 diameters away from the cylinder.This is what has been done in this paper by using the pulsed laser holographic interferometry for several shock Mach numbers of the impinging shock. Results for several moments are shown,giving more know- ledge about the whole unsteady flow field.This is useful for a reliable and complete understanding of the changing force acting on the cylinder,and provides interesting data to check the performance of many recently developed high resolution numerical methods for unsteady shock wave calculation.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

Jet formation in shock-heavy gas bubble interaction

The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analy- sis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pres- sure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.

Demonstrating grating-based phase-contrast imaging of laser-driven shock waves

Single-shot X-ray phase-contrast imaging is used to take high-resolution images of laser-driven strong shock waves.Employing a two-grating Talbot interferometer,we successfully acquire standard absorption,differential phase-contrast,and dark-field images of the shocked target.Good agreement is demonstrated between experimental data and the results of two-dimensional radiation hydrodynamics simulations of the laser-plasma interaction.The main sources of image noise are identified through a thorough assessment of the interferometer’s performance.The acquired images demonstrate that grating-based phase-contrast imaging is a powerful diagnostic tool for high-energy-density science.In addition,we make a novel attempt at using the dark-field image as a signal modality of Talbot interferometry to identify the microstructure of a foam target.

STUDY OF SWEPT SHOCK WAVE AND BOUNDARY LAYER INTERACTIONS

This paper presents briefly the recent progress on study of swept shock wave/boundary layer interactions with emphasis on application of zonal analysis and correlation analysis to them. Based on the zonal analysis an overall framework of complicated interaction flow structure including both surface flowfield and space flowfield is discussed. Based on correlation analysis the conical interactions induced by four families of shock wave generators have been discussed in detail. Some control parameter and physical mechanism of conical interaction have been revealed. Finally some aspects of the problem and the prospects for future work are suggested.

SOUND GENERATION AND INTERACTIONS OF SHOCK WAVES WITH ROWS OF VORTICES

Interactions of shock waves and rows of vortices are studied by solving the two-dimensional,compressible Euler equations with a fifth-order weighted essentially non-oscillatory finite difference scheme.For a compressible flow the Mach number of the shock wave and vortex equals to 1.05 and 0.25,respectively.The resulting flow field contains complex shock structures,such as multiple shock focusing and reflecting regions.At the meantime,sound waves are generated,interrupted and reformed when they touch the main and reflected shock waves.

On the Wake Flow Interaction between Model Turbines with Varying Streamwise Distance

Wind tunnel measurements using particle image velocimetry have been performed around two perforated discs, with varying streamwise distance, in order to simulate the wake interaction between wind turbines. The static pressure footprint (p-f) on ground level associated with the wake behind the disc and wake velocity data for both the streamwise and wall-normal velocity components with the corresponding turbulence intensities are reported. The p-f method shows that the size of the wake regions, behind the wind turbine models, initially drop when a second disc is placed just downstream of the first one. From a mutual distance (Δ χ) of about five disc diameters (5D), both wake footprints increase as the mutual distance is increased, and for very large mutual distances, approximately Δ χ/ D > 15, the footprint of the downstream disc has recovered and is about the same as for a single disc. At last we conclude that despite very different inlet conditions to the discs, with about 50% of reduced velocity on the centre line upstream of the second disc and an increase of the maximum streamwise fluctuations by 90%, the mean velocities in the wake are proven to scale with the hub height velocity.

Numerical Simulations of Shock-Shock Interactions

We present a computational study of Edney type shock-shock interactions between an oblique shock and a bow shock in front of a circular cylinder. Both cold and hot hypersonic test cases were considered and the results revealed the main features characterizing the type III and type IV of interaction, without and with the jet impinging on the cylinder. The simulations also predicted qualitatively the complex flow structure observed in the experiments and the pressure and heat peak on the surface of the cylinder.

Study of interaction between shock wave and unsteady boundary layer

This paper reports theoretical and experimental study of a new type of interaction of a moving shock wave with an unsteady boundary layer. This type of shock wave-boundary layer interaction describes a moving shock wave interaction with an unsteady boundary layer induced by another shock wave and a rarefaction wave. So it is different from the interaction of a stationary shock wave with steady boundary layer, also different from the interaction of a reflected moving shock wave at the end of a shock tube with unsteady boundary layer induced by an incident shock. Geometrical shock dynamics is used for the theoretical analysis of the shock wave-unsteady boundary layer interaction, and a double-driver shock tube with a rarefaction wave bursting diaphragm is used for the experimental investigation in this work.

THE INTERACTION OF A SHOCK WAVE WITH THE BOUNDARY LAYER IN A REFLECTED SHOCK TUNNEL

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.

THE INTERACTIONS OF SHOCK WAVES OF NONSTRICTLY HYPERBOLIC SYSTEMS

The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: [GRAPHICS] The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena.

HEATING CHARACTERISTICS OF BLUNT SWEPT FIN-INDUCED SHOCK WAVE TURBULENT BOUNDARY LAYER INTERACTION

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Numerical Simulation of Shock Bubble Interaction with Different Mach Numbers

The interaction of a shock wave with a spherical helium bubble is investigated numerically by using the high- resolution piecewise parabolic method （PPM）, in which the viscous and turbulence effects are both considered. The bubble is of the same size and is accelerated by a planar shock of different Mach numbers （Ma）. The re- suits of low Ma cases agree quantitatively with those of experiments [G. Layes, O. Le M4tayer. Phys. Fluids 19 （2007） 042105]. With the increase of Ma, the final geometry of the bubble becomes quite different, the com- pression ratio is highly raised, and the time-dependent mean bubble velocity is also influenced. The compression ratios measured can be well normalized when Ma is low, while less agreement has been achieved for high Ma cases. In addition, the mixedness between two fluids is enhanced greatly as Ma increases. Some existed scaling laws of these quantities for the shock wave strength cannot be directly applied to high Ma cases.